Geodesic
Experimental study of some solvers of 3D boundary
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 429-440

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An experimental study of the efficiency of 3D boundary value problem solvers on the regular subgrids of quasi-structured parallelepipedal grids has been carried out. Five solvers are considered: three iterative: the successive over-relaxation method, the implicit alternating direction method, the implicit incomplete factorization method with acceleration by conjugate gradients, as well as two direct methods: PARDISO and HEMHOLTZ — both from the Intel MKL library. The characteristic features of the conducted research are the following: 1) the subgrids contain a small number of nodes; 2) the efficiency is estimated not only for single calculations, but also mainly for a series of calculations, in each of which a large number of repetitions of solving the problem with different boundary conditions on the same same subgrid. On the basis of numerical experiments, the fastest solver under the given conditions was revealed, which turned out to be the method of successive over-relaxation method. 
@article{SJVM_2022_25_4_a7,
     author = {I. A. Klimonov and V. M. Sveshnikov},
     title = {Experimental study of some solvers of {3D} boundary},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {429--440},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a7/}
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I. A. Klimonov; V. M. Sveshnikov. Experimental study of some solvers of 3D boundary. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 429-440. http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a7/